Pre-Algebra Examples

$\frac{4 (x + 4)}{8} = 3 x - 3$

Step 1

Cancel the common factors.

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Step 1.1

Factor $4$ out of $8$ .

$\frac{4 (x + 4)}{4 \cdot 2} = 3 x - 3$

Step 1.2

Cancel the common factor.

$\frac{4 (x + 4)}{4 \cdot 2} = 3 x - 3$

Step 1.3

Rewrite the expression.

$\frac{x + 4}{2} = 3 x - 3$

Step 2

Multiply both sides by $2$ .

$\frac{x + 4}{2} \cdot 2 = (3 x - 3) \cdot 2$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $2$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{x + 4}{2} \cdot 2 = (3 x - 3) \cdot 2$

Step 3.1.1.2

Rewrite the expression.

$x + 4 = (3 x - 3) \cdot 2$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $(3 x - 3) \cdot 2$ .

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Step 3.2.1.1

Apply the distributive property.

$x + 4 = 3 x \cdot 2 - 3 \cdot 2$

Step 3.2.1.2

Multiply.

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Step 3.2.1.2.1

Multiply $2$ by $3$ .

$x + 4 = 6 x - 3 \cdot 2$

Step 3.2.1.2.2

Multiply $- 3$ by $2$ .

$x + 4 = 6 x - 6$

Step 4

Solve for $x$ .

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Step 4.1

Move all terms containing $x$ to the left side of the equation.

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Step 4.1.1

Subtract $6 x$ from both sides of the equation.

$x + 4 - 6 x = - 6$

Step 4.1.2

Subtract $6 x$ from $x$ .

$- 5 x + 4 = - 6$

Step 4.2

Move all terms not containing $x$ to the right side of the equation.

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Step 4.2.1

Subtract $4$ from both sides of the equation.

$- 5 x = - 6 - 4$

Step 4.2.2

Subtract $4$ from $- 6$ .

$- 5 x = - 10$

Step 4.3

Divide each term in $- 5 x = - 10$ by $- 5$ and simplify.

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Step 4.3.1

Divide each term in $- 5 x = - 10$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{- 10}{- 5}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $- 5$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{- 10}{- 5}$

Step 4.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 10}{- 5}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Divide $- 10$ by $- 5$ .

$x = 2$